We report on the measurement of optical isotope shifts for 38, 39, 42, 44, 46–51 K relative to 47 K from which changes in the nuclear mean square charge radii across the <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>28</mn></math> shell closure are deduced. The investigation was carried out by bunched-beam collinear laser spectroscopy at the CERN-ISOLDE radioactive ion-beam facility. Mean square charge radii are now known from 37 K to 51 K, covering all <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>ν</mi><msub><mrow><mi>f</mi></mrow><mrow><mn>7</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msub></math> -shell as well as all <math altimg="si3.gif" xmlns="http://www.w3.or...